Browsing by Author "Segui-Gasco, Pau"
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Item Open Access Decentralised multi-robot task allocation algorithms.(2017) Segui-Gasco, Pau; Shin, Hyo-Sang; Tsourdos, AntoniosMulti Robot Systems (MRS) are gaining increasing popularity both in the research community and in industry. A fundamental problem that underpins the effective coordinated operation of these systems is Task Allocation. To solve this problem, the MRS should be able to find an answer quickly, reliably, and effectively to the question: "given the robots available in the system and the tasks that ought to be carried out, what is the best allocation of these tasks among us?". In this thesis we focus on solving this problem in the decentralised setting, that is, when each agent only has access to its own utility function and does not have any knowledge of the functions corresponding to other agents, i.e.the utility function is local or private. Our algorithms are based on improved versions of the measured continuous greedy algorithm for general matroid-constrained submodular maximisation. The first improvement is a new and smoother increment rule that enables us to reduce the number of steps required to solve the relaxation. The second improvement is to adapt the Decreasing-Threshold procedure for monotone submodular functions to work with non-monotone submodular functions. Then, we present the first decentralised algorithm with constant-factor approximation guarantees for general submodular task allocation. Our algorithm provides an approximation factor of 1-1/e-4ϵ (≈63%) for monotone submodular utilities, and a factor of (1/e-3ϵ) (≈37%) for non-monotone submodular functions. To illustrate the possibilities enabled by non-monotone submodular task allocation, we present a submodular task allocation model for a multi-UAV surveillance mission. Our model features the allocation of heterogeneous surveillance tasks to a heterogeneous multi-UAV team under risk of enemy detection. We develop the model and present proofs to show that it is non-monotone submodular. Then, we run numerical experiments to study the effect of different parameters of our algorithm and compare its performance against the state-of-the- art. To conclude the thesis, we take a completely different approach, the key idea is to trade constant-factor approximation guarantees in exchange for flexibility. We present a preliminary framework based on combinatorial auctions that can transfer centralised solution method to the decentralised Task Allocation domain while requiring a polynomial number of communication rounds. In other words, our framework provides a way to transfer successful methods to solve NP-Hard problems such as Metaheuristics, Mixed-Integer Programming, Constraint Programming, etc. to the decentralised setting.Item Open Access Fast non-monotone submodular maximisation subject to a matroid constraint(2017-03-21) Segui-Gasco, Pau; Shin, Hyo-SangIn this work we present the first practical . 1 e −ǫ . -approximation algorithm to maximise a general non-negative submodular function subject to a matroid constraint. Our algorithm is based on combining the decreasing-threshold procedure of Badanidiyuru and Vondrak (SODA 2014) with a smoother version of the measured continuous greedy algorithm of Feldman et al. (FOCS 2011). This enables us to obtain an algorithm that requires O( nr2 ǫ4 . ¯ d+ ¯ d ¯ d .2 log2 ( n ǫ )) value oracle calls, where n is the cardinality of the ground set, r is the matroid rank, and ¯ d, ¯ d ∈R+ are the absolute values of the minimum and maximum marginal values that the function f can take i.e.: − ¯ d ≤fS(i) ≤ ¯ d, for all i ∈E and S ⊆E, where E is the ground set. The additional value oracle calls with respect to the work of Badanidiyuru and Vondrak come from the greater spread in the sampling of the multilinear extension that the possibility of negative marginal values introduce.